Are there any 4 letter words (or greater) in English that are complete anagrams? That is, that spell a valid word no matter what order the letters are rearranged into.

welcome, Pook!

interesting question. I have no answer.

I suspect the answer is no (at least for four letters) but no one has ever been able to tell me for sure.

And thanks for the welcome! Just finding my way around. It's a bit confusing with this rather archaic interface that it makes it hard to find whether topics like this have been covered before, so apologies if it has somewhere.

Hi Pook,

I don't know of any off hand. This is one of those interesting questions that'll get all of us scouring the corners of our brains, though.

Welcome.

no matter what order the letters are rearranged into. You mean if the word is 1234, then 1324, 1423, 4321, 3214, 2314, etc. would all be words? Yow.

Yes, sixteen anagrams from four letters. Or twenty five words from five letters.

read
dear
rade*
Edar
dare
ader *

* ader wax n. A waxy mineral that is a mixture of hydrocarbons and occurs in association with petroleum; some varieties are used in making ceresin and candles;

* Rade \Rade\ (r[=a]d), n.
A raid. [Scot.]
[1913 Webster]

16? That would mean 4 words starting with D, 4 with E, 4 with A and 4 with R , if you would consider the word 'read'?
I've got six. Impossible task it seems.
Although I'm not good at what seems like mathematics to me, I'm interested.

There would have to 24 words to satisfy the condition. In general the number of combinations possible for n letters is n!, such as in this case, 4 x 3 x 2 x 1.

1234 , 2134 , 3124 , 4123
1243 , 2143 , 3142 , 4132
1324 , 2314 , 3214 , 4213
1342 , 2341 , 3241 , 4231
1423 , 2413 , 3412 , 4312
1432 , 2431 , 3421 , 4321

The best I can come up with is east, teas, eats, seat, and sate, and I suppose we could also add tase, as in Don't tase me, bro! although that would be stretching it.

I'm obviously better at words than maths too - yeah 24, not 16. You're right, it's a factorial progression.

I agree, even 16 is not likely, let alone 24.

How about a three letter word?
You would only need six for that:

123
132
213
231
312
321

For five letters you would need:

6x1-2s 6x2-1s 6x3-1s 6x4-1s 6x5-1s
6x1-3s 6x2-3s 6x3-2s 6x4-2s 6x5-2s
6x1-4s 6x2-4s 6x3-4s 6x4-3s 6x5-3s
6x1-5s 6x2-5s 6x3-5s 6x4-5s 6x5-4s

which equals 120 words!

Interesting mathematical progression then:
letters=words
2=2
3=6
4=24
5=120

and then I guess
6=120x6=720
7=720x7=5040
...and so on

well, you could try words with repeated letters -- that would make the task somewhat easier.

-joe (reductio ad absurdum) friday

some sort of factorial Fibonacci?

a two-letter word which works: aa

-joe (me/em) friday

for three ate gets close?

eat
ate
tea

then
tae (maybe?)
aet
ata
and my favorite:

ETA

I wouldn't make it seem that complicated. It's simply a matter of the factorial of any number. Suppose you have an 8 letter word. For the first position, you have eight choices. Once you've chosen the first letter, you now have 7 letters left over to choose from for the second letter in the word, and so on, so that the number of possible choices for a given position decreases by one each time. Hence 8 x 7 x 6 x 5 x 4 x3 x 2 x 1 = 8! = 40320 combinations of 8 letters. It naturally follows that 9! will be 9 times 8! and so on.

Remove the restriction to using just the English language and you probably will have better odds.

Actually, I think you can pretty much eliminate all 3 or more letter words with repeated letters because one of the combinations is going to be starting with the two repeated letters and another is going to end with the two repeated letters.

There are some words end in double letters (butt, ass, ...) but not too many start with double letters (aardvark, oocyst, ... um... ). I don't think those two sets are going to intersect.

Oo, good point.

I thought the factorial of a number was the ADDITION of all previous numbers, not the multiplication of them?
That is, !8 = 1+2+3+4+5+6+7+8=36
It is a factorial multiplication, whatever the technical term for that is, but not THE factorial of the number. I think?

I think the word you're looking for is factorial.

No.

>you can pretty much eliminate all 3 or more letter words

ooh.. oho! hoo!!

-joe (good point, though) friday

OK, you're right I'm wrong, like I said I'm not good at remembering maths. So what is the addition of the numbers called then?

I guess you are talking about triangular numbers:

T(1) = 1
T(2) = 1 + 2 = 3
T(3) = 1 + 2 + 3 = 6
T(n) = 1 + 2 + 3 + ... + (n-1) + n

Yes, it's all coming vaguely back to me now.

And the fact that 10 is a triangular number and we use base ten is what gives the number 9 (10-1) its special properties, like if you multiply it by any whole integer above zero and then add the digits of the answer until you get back to one digit again it's always 9. Or something like that. But this is a word forum not a number forum so i'd better shut up now.

Another interesting question is: What is the longest sentence that is grammatical through all its possible permutations?

What do you mean? There are many ways you can change (ie 'permute') a sentence. Do you mean word order? Clause order? Anagramise it? What?

In the spirit of common sense I'd go with word order. Would it include changing of parts of speech? E.g., S V O Dog bites man S V O Bites dog man Adj S V Dog man bites Adj S V Man dog bites etc.

I'd go with word order

Though, I, too, thought of word order, rearranging higher constituents might be interesting. Some might sound a bit yoda-ish: Nearly everybody likes strawberry ice cream => Strawberry ice cream, nearly everybody likes. Doing it at the word level, would be more difficult in more highly inflected languages (e.g., Russian, Latin) and easier in less (e.g., Chinese). Actually, in Russian or Latin, moving the words around would not change the general meaning of the sentence. In Chinese, words are commonly adjectives, nouns, and verbs.

>Some might sound a bit yoda-ish

Absolutely. But I was just thinking there are some sets of words that are grammatical in almost every possible order. Best approach would be to think of words that are homographs of other words and have lots of meanings.

This is not the best example of that, but...

It will say “you”.
“It”, you say, Will?
It? Say “Will”, you!
Will it say “you”?
Will you say it?
“Will it”, you say?
Say it, will you?
Say you will it!
You say it, Will.
You say it will.

etc.

What is the longest set of words with the most permutations?

Probably not an answerable question. But we can die trying...

...But can we die not trying an answerable question? Probably.

If Had had had "had had" where Has had had "has had", had Had had Has?

And that's a sentence?

No only a question.

Easy. I remember this from the schoolyard.

Has and Had are sitting a grammar test. The correct answer to number X is either "had had" or "has had." Had put the former, Has the latter. So it depends on which answer is correct, and what their final score for the test was. In the phrasing I remember, which was a little longer, the answer is given, and Had has had Has.

See also this and this.

What school did you go to??? We never got beyond Pete and his peppers.

Actually, it was something like, "Put put put put and put put put put but put was the correct answer." With punctuation: "Put put "put" and Put-Put put "put put" but "put" was the correct answer.

Wow. We were silly.